Critical branching random walk in $\mathbb{Z}^{d}$

Speaker: 陈昕昕（北京师范大学）

Title: Critical branching random walk in $\mathbb{Z}^{d}$ 

Inviter: 随机分析研究中心

Language: English 

Time & Venue: 2026 年9月4日10:30–11:30 南楼613

Abstract: We study the critical branching random walk on $\mathbb{Z}^{d}$, started from a distant point $x$ and conditioned to hit some compact set $K$ in $\mathbb{Z}^{d}$. We are interested in the occupation time in $K$ and present its asymptotic behaviors in different dimensions. It is shown in this work that the occupation time is of order $\lVert x\rVert^{4-d}$ in dimensions $d\leq 3$, of order $\log\lVert x\rVert$ in dimension $d=4$, and of order $1$ in dimensions $d\geq 5$. The corresponding weak convergences are also established. These results answer a question raised by Le Gall and Merle (ECP, 2006). This is based on the joint work with Shen Lin.